Langlands Reciprocity for Algebraic Surfaces
| dc.creator | Ginzburg, Victor | |
| dc.creator | Kapranov, Mikhail | |
| dc.creator | Vasserot, Eric | |
| dc.date | 1995-02-20 | |
| dc.date.accessioned | 2026-07-07T09:16:29Z | |
| dc.date.available | 2026-07-07T09:16:29Z | |
| dc.description | This note is an attempt to extend "Geometric Langlands Conjecture" from algebraic curves to algebraic surfaces. We introduce certain Hecke-type operators on vector bundles on an algebraic surface. The crucial observation is that the algebra generated by the Hecke operators turns out to be a homomorphic image of the {\it quantum toroidal algebra}. The latter is a quantization, in the spirit of Drinfeld-Jimbo, of the universal enveloping algebra of the universal central extension of a "double-loop" Lie algebra. This yields, in particular, a new geometric construction of affine quantum groups of types A, D E in terms of Hecke operators for an elliptic surface. | |
| dc.description | 13 pages, submitted to Mathematical Research Letters | |
| dc.identifier | https://arxiv.org/abs/q-alg/9502013 | |
| dc.identifier | http://arxiv.org/abs/q-alg/9502013 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/153366 | |
| dc.subject | Quantum Algebra | |
| dc.subject | Algebraic Geometry | |
| dc.title | Langlands Reciprocity for Algebraic Surfaces | |
| dc.type | text |